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IC-NRLF 


SB    17    537 


\>i  r   i 

AY  15 


Scientific  Grading  of  College  Students 

RAYMOND  W.  Sn*s 

PROFESSOR  OF  SCHOOL  ADMINISTRATION 

SCHOOL  OF  EDUCATION,  UNIVERSITY  OF  PITTSBURGH 


An  address  before  the  Conference  of  College  Presidents 
of  Pennsylvania,  Feb.  29,  1912,  held  on  the  occasion 
of  the  celebration  of  the  one  hundred  twenty-fifth 
anniversary  of  the  University;  of ; Pittsburgh.'. 


Reprinted  from 

UNIVERSITY  OF  PITTSBURGH  BULLETIN 
Vol.  8,  No.  21 


SCIENTIFIC  GRADING  OF  COLLEGE  STUDENTS 

RAYMOND  W.  SIES 

PROFESSOR  OF  SCHOOL  ADMINISTRATION 

UNIVERSITY  OF  PITTSBURGH 


Mr.  Chairman: 

President  William  T.  Foster  of  Reed  College  in  his 
recent  book,  "The  Administration  of  the  College  Curricu- 
lum," opens  an  important  chapter  bearing  upon  the  sub- 
ject treated  in  this  paper  with  the  following  paragraph : — 

"College  honors  are  everywhere  awarded  on  the  naive 
assumption  that  grades  in  college  courses  are  distributed 
on  a  scientific  basis.  For  many  important  administrative 
purposes  we  assume  that  an  A  in  one  course  is  equivalent 
to  an  A  in  another  course ;  that  the  80  per  cent  of  one  in- 
structor indicates  an  achievement  equal  to  the  80  per  cent 
of  another  instructor.  Accordingly  we  estimate  the  fitness 
of  candidates  for  admission,  determine  eligibility  for  ath- 
letics, assign  annually  hundreds  of  thousands  of  dollars  in 
scholarships  and  fellowships,  award  Commencement 
honors,  elect  men  to  Phi  Beta  Kappa,  and  confer  degrees 
wholly  or  in  large  part  on  the  evidence  secured  by  merely 
counting  the  number  of  A's,  the  number  of  B's,  and  so 
forth,  that  each  student  has  to  his  credit.  The  question 
is  pertinent  to  what  extent  our  assumption  of  the  equiva- 
lency of  grades  is  warranted  by  the  facts.'** 


Op.  cU.,  pp.  ««,. 


If  the  answer  to  this  question  propounded  by  Dr. 
Foster  is,  as  he  intimates  in  his  opening  statement, 
that  our  assumption  is  without  foundation,  the  further 
question  immediately  suggests  itself  whether  anything  can 
be  done  to  bring  a  degree  of  order  out  of  the  relatively 
chaotic  condition  of  affairs  described.  The  present  paper 
has  to  do  with  the  problems  raised  by  these  questions. 

Fundamental  to  the  entire  discussion  are  the  scientific 
principles  in  accordance  with  which  mental  abilities  or 
achievements  are  actually  distributed  among  college  stud- 
ents. It  is  a  matter  of  common  experience  that  human 
beings,  even  those  of  the  same  sex  and  approximate  age, 
vary  greatly  among  themselves.  The  variation  is  far 
greater  in  mental  than  in  physical  traits.  Men  differ  much 
more  widely  in  intellect  and  temperament  than  in  height, 
chest  capacity,  or  cephalic  index.  The  same  variation 
prevails  among  plant  and  animal  species  and  in  general 
throughout  nature.  This  variation,  however,  does  not 
represent  so  much  chaos  and  confusion  in  nature  (inclu- 
sive of  man)  ;  it  does  not  represent  an  unpredictable  and 
unmanageable  phenomenon  which  the  scientist  recognizes 
as  merely  a  source  of  constant  disturbance  and  irritation. 
For  the  most  part  the  facts  are  quite  the  contrary.  In 
fact,  the  variations  in  question  are  controlled  in  a  large 
measure  by  natural  law,  and  the  scientist  has  equipped 
himself  with  the  principles  involved. 

It  has  been  found/  by  many  tests  that  physical  traits 
of  animals  and  men  of  a  given  species  tend  to  be  dis- 
tributed in  accordance  with  the  distribution  of  a  recur- 
rent variable  quantity  resulting  from  the  chance  action  in 
different  combinations  of  a  very  great  number  of  equal 
independent  causes,  each  just  as  likely  to  occur  in  any 
given  case  as  not.  The  ordinary  graphic  representation 
of  such  a  distribution,  known  as  a  normal  distribution,  is 
the  normal  probability  curve.  In  figure  i  we  have  an  il- 
lustration of  this  curve.  The  abscissas  represent  the  dif- 
ferent magnitudes  of  the  variable  and  the  ordinates  the 
frequency  of  occurrence  of  these  magnitudes.  It  will  be 
noted  that  the  magnitudes  cluster  closely  about  a  mean 
or  norm  and  that  on  each  side  of  this  central  tendency, 


0 


Fig.  I 

indicated  by  the  apex  of  the  curve,  the  frequencies  grad- 
ually decrease  to  zero.  The  relation  between  height  and 
width  varies  in  different  curves,  some  are  taller  and  some 
flatter  than  the  one  before  us ;  but  they  all  belong  to  the 
same  species  and  are,  governed  by  the  same  mathematical 
equation.  This  equation  in  its  simplest  form  is  given  in 
the  figure.  The  area  between  the  curve  and  the  zero  ab- 
scissa is  known  as  the  probability  integral.  The  perfectly 
smooth  and  regular  curve  would  appear  only  if  the  causes 
were  infinite  in  number.  Consequently,  the  actual  curves 
that  investigators  have  secured  have  been  only  approx- 
imations to  the  mathematical  forms.  Figure  2  presents  a 
curve  giving  the  distribution  of  the  heights  in  inches  of 
25,878  recruits  in  the  United  States  army,  as  an  example 
of  the  distribution  of  physical  traits.  It  is  taken  from  one 
of  Pearson's  works.*  The  abscissas  represent  heights, 
the  ordinates  represent  frequency  of  heights.  Such  a  curve 
is  technically  known  as  a  curve  of  frequency,  and  the  area 
between  it  and  the  zero  abscissa  as  a  surface  of  frequency. 
The  approximation  of  the  curve  and  surface  in  question 
to  the  normal  probability  curve  and  the  probability  in- 
tegral is  apparent. 

There  is  much  evidence  that  mental  traits  tend  to  be 
distributed  in  the  same  way.  In  the  first  place  modern 
*  Vide  The  Chances  oj Death,  by  Karl  Pearson,  Vol.  I.,  pp.  276-277. 

3 


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physiological  psychology  teaches  that  mental  traits  have 
a  physical  basis  in  physical  traits  of  the  nervous  system, 
and  are  correlated  with  them.  There  is  no  good  reason 
to  believe  that  variation  in  the  nervous  system  is  essen- 
tially different  from  variation  in  the  muscular  or  other 
system.  It  would  be  anomalous  if  the  parts  and  elements 
of  the  nervous  system  were  distributed  in  accordance  with 
a  law  different  from  the  one  governing  the  distribution 
of  other  physical  traits.  Granting  then  that  variation  in 
the  nervous  system  is  normal,  we  may  argue  on  psycho- 
physical  grounds  that  the  distribution  of  mental  traits 
tends  to  be  of  the  normal  type.  We  may  reasonably  as- 
sume that  mental  traits  follow  the  same  law  of  variation 
as  the  corresponding  physical  traits.  Furthermore,  mental 
phenomena  are  natural  phenomena,  and  their  character  as 
such  is  presumptive  evidence  of  considerable  weight  in 
favor  of  the  position  here  taken. 

Statistical  evidence  in  favor  of  the  tendency  of  mental 
traits  to  be  distributed  in  the  manner  under  consideration 
is  not  so  plentiful  nor  so  definite  on  the  whole  as  that  con- 
cerning physical  traits,  owing,  the  scientist  believes,  to 
the  difficulty  of  adequately  measuring  most  mental  traits 
with  our  present  facilities.  However,  such  evidence  is 
by  no  means  entirely  absent.  Some  specific  mental  traits 
can  be  measured  with  a  fair  degree  of  accuracy,  and  meas- 
urements of  such  traits  in  groups  of  properly  selected  in- 
dividuals have  been  made  and  the  distributions  worked 
out.  When  conducted  by  proper  methods  these  investi- 
gations have  definitely  shown  that  the  particular  traits  in 
question  tend  to  be  normally  distributed.  In  figure  3 
is  presented  the  distribution  of  a  relatively  simple  mental 
trait  in  312  boys  twelve  years  old.  The  trait  in  question 
is  efficiency  in  perceiving  A's  on  a  page  of  capital  letters 
appearing  in  indiscriminate  order.  This  distribution  is 
one  of  a  number  of  the  same  class  given  by  Dr.  Thorn- 
dike.* 

It  is  proper  to  add  that  it  is  an  exceptionally  good  il- 
lustration of  approximation  to  the  normal  distribution 
in  the  field  of  mental  measurements,  especially  in  view 


*Vide  Introdui  tion  to  the  Theory  of  Mental  and  Social  Measurements,  by 
E.  Iy.  Thorndike,  pp.  46,  49,  83. 

5 


Efficiency   in   Perception    of    312.    Boys 

Fiq.3 

of  the  relatively  small  number  of  cases.  However,  the 
weight  of  evidence  from  tests  of  mental  traits  susceptible 
of  fairly  accurate  measurements  is  very  strongly  in  favor 
of  the  proposition  that  such  traits  are  approximately  norm- 
ally distributed.  In  general,  results  leading  to  a  different 
conclusion  may  be  charged  to  defective  methods,  such  as 
the  mixing  of  types  and  the  testing  of  selected  groups. 
Causes  affecting  the  form  of  distribution  other  than  the 
natural  forces  of  variation  must  obviously  be  eliminated. 
The  individuals  tested  must  correspond  in  age  or  maturity 
and  in  the  degree  of  training  previously  received  in  the 
trait  tested.  They  must  also  represent  a  random  selec- 
tion. Obviously  the  distribution  of  a  mental  trait  in  a 
group  of  geniuses  or  a  group  of  idiots  would  not  be  normal. 
The  preceding  considerations  with  others  that  might 
be  advanced  constitute,  in  the  minds  of  scientific  men, 
sufficient  evidence  to  warrant  the  assumption  that  mental 
traits  not  yet  susceptible  of  fairly  accurate  measurement 

6 


tend  to  be  distributed  in  the  form  represented  by  the 
probability  curve.  Experience  thus  far  warrants  the  be- 
lief with  some  confidence  that  when  the  technique  of  quan- 
titative methods  in  the  mental  and  social  sciences  is  suffi- 
ciently developed  the  distribution  of  such  traits  will  be 
found  to  be  not  materially  different  in  form  from  that  of 
the  traits  we  have  been  considering  in  the  preceding  pages. 
In  this  same  connection  Dr.  Thorndike  writes  as  follows: 
j^ral]  do  occur  very  commonly  in  mental  traits  of  original 

"Distributions  aproximating  it  [the  probability  inte- 
nature.  And  one  will  probably  never  be  far  misled  by 
supposing  that,  in  respect  to  the  amount  of  original  en- 
dowments in  any  trait,  individuals  of  the  same  sex,  race 
and  age  are  distributed  approximately  according  to  the 
probability  surface.  The  evidence  from  measurements 
points  toward  such  approximation.  Moreover,  what  is 
known  of  the  physical  basis  of  intellect  and  character  leads 
to  the  expectation  that  many  somewhat  nearly  equal  fac- 
tors are  at  work  to  determine  the  amount  of  any  instinct 
or  capacity  possessed  by  men."* 

We  now  come  directly  to  the  matter  of  distribution 
of  the  ability  or  achievements  of  college  students  in  col- 
lege classes,  which  constitutes  one  of  the  complex  mental 
traits  which  we  have  no  satisfactory  means  of  measuring 
at  the  present  time.  Is  this  ability  or  type  of  achievement 
normally  distributed?  The  grounds  for  assuming  approx- 
imation to  the  normal  distribution  are  just  as  strong  in 
this  case  as  in  the  case  of  other  mental  traits  not  sus- 
ceptible of  fairly  exact  measurement.  Yet  in  the  actual 
grading  of  college  students  by  college  teachers  practically 
all  conceivable  forms  of  distribution  are  manifested.  Ap- 
proximation to  the  normal  distribution  is  the  exception. 
This  diversity,  of  course,  is  due  very  largely  to  the  ab- 
sence of  definite  units  and  the  inadequacy  of  measurement, 
but  it  is  probably  due  more  largely  to  the  widely  varying 
personal  factor  in  the  teachers.  Each  teacher  has  his 
own  particular  views  and  habits  in  grading.  When,  how- 
ever, instead  of  the  grades  of  individual  teachers  we  dis- 
tribute collectively  the  grades  of  a  large  number  of  teach- 
ers in  different  subjects,  the  influence  of  the  personal  fac- 

* Educational  Psychology,  by  E.  L.  Thorndike,  2nd  Ed.,  pp.  165-166. 

7 


Fl    'Con  '  P-  '  P-h  '  F-  '  F-h  '  G-  '  G-h  '  E-  '  £-*• 

Grades    of    12000    Students 
University    of    Wisconsin 


tor  is  practically  eliminated,  since  the  peculiarities  in,  the 
grading'  of  one  teacher  are  neutralized  by  those  of 
another.  Such  a  distribution  may  therefore  IDC  expected 
to  exhibit  a  very  rough  approximation  to  the  normal. 

In  figure  4  are  exhibited  about  12,000  general 
averages  of  students  in  the  University  of  Wisconsin 
in  recent  years.*  These  averages  were  computed  from  the 
grades  of  a  large  number  of  teachers.  The  figure  exhibits 
a  distinctly  imperfect,  but  yet  quite  recognizable,  approx- 
imation to  the  probability  integral.  The  relatively  large 
divergence  therefrom  may  fairly  be  charged  very  largely 
to  the  present  unavoidable  imperfections  of  the  scale  or 
scales  wherewith  ability  of  achievement  in  the  classroom 
must  be  measured.  President  Foster  in  the  book  cited  at 
the  beginning  has  presented  a  study  of  nearly  12,000  dif- 
ferent annual  grades  in  many  different  subjects  secured 
by  students  in  Harvard  College  during  the  years  1903-4 
and  1904-5. t  The  distribution  of  these  grades  on  a  scale 
with  five  divisions  is  similar  in  form  to  that  of  the  general 
averages  of  the  Wisconsin  students. 

How  widely  the  grading  of  individual  teachers  di- 
verges from  the  standard  form  may  be  judged  from  table 
I  for  which  Professor  Max  Meyer  of  the  University  of 
Missouri  is  responsible.  This  table  shows  the  distribution 
of  the  four  grades,  A,  B,  C,  and  F,  in  use  at  the  University 
of  Missouri,  by  forty  individual  teachers  in  that  institution 
during  a  period  of  five  years  preceding  1908.  For  the 
most  part  the  grades  were  given  for  courses  in  the  College 
of  Arts  and  Science,  and  therefore  to  a  large  extent  the 
different  teachers  had  the  same  students.  To  avoid  undue 
publicity  the  teachers  are  designated  by  subjects.  On  the 
basis  of  the  grades  assigned  the  students  graded  by  each 
teacher  were  divided  into  three  groups  designated  super- 
ior, medium,  and  inferior.  The  first  group  comprised  the 
twenty-five  per  cent  of  students  ranking  highest,  the  last 
group  the  twenty-five  per  cent  ranking  lowest,  and  the 
middle  group  the  remaining  fifty  per  cent  ranking  between 
the  other  groups.  The  last  column  indicates  the  total 
number  of  students  graded  by  each  teacher.  The  distri- 
'  xvidfTSchool  and  University  Grades,  by  Walter  F.  Dearborn,  Bulletin  of 

the  University  of  Wisconsin,  High  School  Series,  No.  9,  pp.  43,  44,  46. 
/    fVide  Administration  of  the    College  Curriculum,  by  W.  T.  Foster,   pp. 

251  ff.,  276  if.  9 


bution  of  grades  is  indicated  by  the  percentages  of  the 
total  number  of  students  receiving  the  different  grades  in 
the  several  groups.  The  teachers  are  listed  in  the  order  of 
their  liberality  of  grading.  Thus  the  first  teacher  assigned 
the  grade  A  not  only  to  all  his  superior  students,  but  to 
considerably  more  than  half  of  his  medium  students  as 
well.  He  also  assigned  the  grade  B  to  more  than  half  his 
inferior  students,  and  few  were  failed.  The  last  teacher, 
on  the  other  hand,  assigned  the  grade  A  to  only  one  per 
cent  of  all  his  students,  and  over  one  half  of  his  superior 
students  received  the  grade  C.  All  his  inferior  students 

Table  I 

Grading  of  Students  at  the 
University  of  Missouri. 


Teachers 

25  Per  Cent 
Superior 
Students 

50  Per  Cent 
Medium 
Students 

25  Per  Cent 
Inferior 
Students 

Total  Number 
of  Students 

A 

B 

C 

A 

B 

C 

F 

B 

C 

F 

2b 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
20 
22 
14 
21 
19 
25 
20 
18 
23 
21 
13 
11 
24 
22 
9 
18 
19 
25 
20 
19 
16 
13 
18 
18 
16 
9 
1 

6 
3 
11 

4 
6 

5 
7 
2 
4 
12 
14 
1 
3 
16 
7 
6 

5 
6 
9 
12 
7 
7 
9 
16 
11 

13 

30 
27 
27 
15 
14 
14 
11 
11 
9 
7 
5 
5 
1 

20 
23 
23 
31 
36 
26 
39 
29 
30 
29 
39 
36 
38 
50 
45 
42 
41 
41 
40 
40 
40 
38 
37 
37 
37 
36 
34 
32 
31 
30 
29 
28 
28 
25 
24 
22 
19 
17 
12 

«• 
4 

10 

10 
11 
14 
6 
9 
11 

5 
8 
9 
9 
10 
10 
10 
12 
13 
13 
13 
14 
16 
18 
19 
20 
21 
22 
22 
25 
26 
28 
31 
33 
35 
47 

3 
3 

13 
19 

7 

1 
1 

6 

10 
6 
13 
12 
19 
14 
19 
15 
16 
9 
14 
15 
14 
19 
17 
19 
19 
20 
20 
21 
15 
19 
17 
20 
20 
17 
12 
25 
16 
6 
15 
18 
14 
10 
16 
13 
11 
13 

2 

5 
13 
5 
11 
5 
10 
9 
15 
11 
10 
11 

8 
6 
6 
5 
5 
4 
10 
6 
8 
5 
5 
8 
13 

9 
19 
10 
7 
11 
15 
9 
12 
14 
12 
25 
25 

623 
130 
958 
208 
461 
287 
577 
295 
592 
145 
586 
907 
941 
917 
293 
779 
479 
238 
685 
263 
506 
205 
964 
225 
806 
250 
441 
21 
266 
182 
380 
426 
544 
209 
813 
558 
495 
826 
1098 
1903 

Latin    I    

ithematics    I  

eek                

tin    II          

A-  *  ench                  

Political  Science  
Mathematics    II   .. 

German    II 

Geology     

History    I          

History  of  Art   

Bacteriology          •      • 

Freehand  Drawing.  .  . 

English    I    

Astronomy   

History    II 

Zoology    II  

German    III    

Chemistry    II  

Education 

Mathematics,  III  
Mathematics,  IV  
Physiology   

Mathematics,  V  
Engineering    I    .      ... 

Mechanical  Drawing. 
Mechanics  

English    II          

Chemistry,  III  

10 


were  failed  and  some  of  his  medium  students.  The  table 
shows  all  degrees  of  leniency  and  severity  between  these 
extremes.  By  reference  to  the  last  column  we  find  that 
every  teacher  almost  without  exception  had  a  sufficient 
number  of  students  during  the  five  years  to  warrant  the 
belief  that  the  distribution  of  actual  ability  or  achieve- 
ment in  his  classes  was  approximately  normal.*  The  chaos 
and  gross  injustice  of  such  grading  are  evident  and  re- 
quire no  comment. 

It  should  be  understood  that  there  is  nothing  strange 
or  peculiar  about  the  state  of  affairs  here  described  which 
formerly  existed  in  the  University  of  Missouri.  It  is  simply 
typical  of  the  situation  at  practically  all  colleges  and  uni- 
versities throughout  the  country.  The  natural  remedy 
for  this  condition  of  things  with  its  confusion  and  injustice 
is  plainly  the  normal  or  scientific  distribution  of  students' 
grades  which  requires  teachers  to  dispense  grades  accord- 
ing to  the  natural  distribution  of  ability  or  achievement. 
A  few  progressive  institutions,  as  indicated  below,  have 
recently  begun  breaking  the  way  toward  better  things  by 
the  adoption  of  this  device.  Among  these  the  university 
just  mentioned  must  be  given  the  leading  place. 

There  are  some  persons  without  doubt  to  whom  the 
preceding  considerations  will  not  appear  convincing. 
Despite  the  above  argument  of  numbers  they  will  be  in- 
clined to  insist  that  the  striking  and  well-nigh  universal 
differences  in  the  distribution  of  grades  by  different  teach- 
ers are  to  be  explained  primarily  by  the  fact  that  some 
teachers  and  some  subjects  consistently  draw  a  better 
grade  of  students  than  others.  In  considering  this  ob- 
jection it  is  necessary  to  distinguish  carefully  between 
required  and  elective  courses.  In  the  first  place,  if  the  ob- 
jection is  sound,  if  variations  among  teachers  in  the  dis- 
tribution of  grades  are  primarily  due  to'differences  in  the 
quality  of  the  students,  we  should  expect  a  degree  of  uni- 
formity in  the  distribution  of  the  grades  assigned  by  dif- 
ferent teachers  of  required  courses.  This  relative  uni- 
formity, however,  does  not  seem  to  exist.  Our  experience 
does  not  bear  out  the  assumption  that  it  exists,  and  inves- 


*Vide  The  grading  of  students,  by   Max  Meyer,  Science,  n.  s.,    Vol.  28 
pp.  243  ff. 

11 


tigators  have  not  recorded  any  observed  differences,  so  far 
as  the  writer  is  aware,  between  the  discrepancies  among 
teachers  in  grading  students  in  required  courses  and  those 
in  grading  students  taking  elective  courses. 

Again,  if  the  objection  under  consideration  is  sound, 
we  should  expect  that  teachers  of  elective  courses  who 
habitually  grade  higher  than  the  average  teacher,  do  really 
have  superior  students,  and  those  who  habitually  grade 
correspondingly  low  really  have  inferior  students.  The 
facts,  however,  so  far  as  they  have  been  definitely  ascer- 
tained, are  rather  the  reverse.  In  table  II  are  presented 
the  results  of  an  investigation  made  by  Dean  Ferry  of 
Williams  College  upon  this  specific  problem.  The  admin- 
istration of  the  curriculum  at  Williams  College  is  more 
than  ordinarily  favorable  for  the  prosecution  pf  such 
a  study.  In  the  freshman  and  sophomore  years  the  stud- 
ies are  either  prescribed  or  elective  within  narrow  limits. 
In  the  junior  and  senior  years  there  is  practically  free 
election.  Dean  Ferry  computed  the  average  standings 
secured  during  their  freshman  and  sophomore  years  by 
the  several  students  enrolled  in  all  the  junior  and  senior 
elective  courses  of  the  college  offered  during  the  years 
1906-1907,  1907-8,  and  1908-9.  On  the  basis  of  these 

Table  II 

Quality  of  Grading  and  of  Students  at  Williams 
College 


Teachers 

Quality  of 
Grading 

Quality  of 
Students 

Teachers 

Quality  of 
Grading- 

Quality  of 
Students 

1 

120 

-  7 

16 

41 

2 

2 

114 

-30 

17 

41 

9 

3 

95 

-17 

18 

40 

-14 

4 

89 

-22 

19 

34 

15 

5 

89 

-  6 

20 

32 

7 

6 

73 

-40 

21 

27 

77 

7 

66 

-33 

22 

23 

39 

8 

63 

5 

23 

20 

13 

9 

59 

-  8 

24 

6 

-  2 

10 

58 

6 

25 

3 

24 

11 

56 

-  1 

26 

0 

113 

12 

52 

-21 

27 

0 

111 

13 

50 

17 

28 

-11 

-  4 

14 

49 

20 

29 

-21 

39 

15 

42 

1 

30 

-23 

41 

12 


earlier  records  he  improvised  a  measure  or  index  of  the 
quality  of  students  in  the  several  junior  and  senior  courses. 
On  the  basis  of  the  quality  of  students  thus  determined 
he  further  improvised  a  measure  or  index  of  the  quality 
or  standard  of  grading  of  each  of  the  thirty  teachers  giving 
junior  and  senior  elective  courses.  The  latter  measure  was 
so  formulated  that  a  high  index  indicates  liberality  in  grad- 
ing and  a  low  index  indicates  corresponding  severity.  Time 
and  space  do  not  permit  here  an  explanation  of  the  deriva- 
tion of  these  indexes.  It  must  suffice  for  the  present  to 
say  that  the  writer  has  satisfied  himself  that,  though  not 
mathematically  exact,  the  indexes  are  fairly  reliable.  Those 
desiring  a  detailed  account  are  referred  to  Dean  Ferry's 
report  for  1910-11,  in  which  the  investigation  is  described.* 
Table  II  is  copied  from  this  report  with  changes  in  the 
order  of  arrangement.  The  data  for  the  different  teachers 
are  here  arranged  in  the  order  of  the  quality  of  grading. 
The  indexes  for  teachers  who  were  most  liberal  in  grading 
head  the  columns,  those  for  the  teachers  most  severe  in 
grading  close  the  table.  It  will  be  observed  that,  whereas 
the  indexes  in  column  two  regularly  decrease,  the  corres- 
ponding indexes  in  column  three  irregularly  increase.  This 
means  that  on  the  whole  the  teachers  who  graded  highest 
had  the  poorest  students  and  those  who  graded  lowest  had 
the  best  students.  The  correlation  between  standard  of 
grading  and  quality  of  students  is  distinctly  negative.  By 
various  methods  of  calculation  the  coefficient  of  correla- 
tion has  a  high  negative  value.  What  is  the  explanation 
of  these  facts?  The  chief  explanation  is  not  far  to  seek. 
The  negative  correlation  between  quality  of  grading  and 
quality  of  students  results  very  largely  from  the  well  known 
proclivity  of  inferior  and  indolent  students  to  seek  snap 
courses  and  the  tendency  of  able  and  earnest  students 
to  seek  the  more  substantial  courses.  A  snap  course  may 
be  defined  as  one  where  for  a  given  effort  or  achieve- 
ment a  relatively  high  grade  may  be  gained,  owing  to  low 
standards  of  qualitative  or  quantitative  requirements,  or 
both.  To  undertake  to  demonstrate  here  that  such  courses 
are  studiously  sought  by  some  students  and  avoided  to 
some  extent  by  others  would  be  a  clear  case  of  carrying 


-Vide   Williams  College  Bulletin,  Series  8,  No.5  (June,  1911),  pp.  27-32. 

13 


coals  to  Newcastle.  Finally  in  this  connection  it  may  be 
said  that  Dean  Ferry's  results  and  the  conclusions  there- 
from are  reinforced  by  results  secured  by  President  Foster 
from  a  study  of  the  undergraduate  history  of  the  4,311 
men  who  graduated  from  Harvard  College  during  the 
years  1886  to  1900  inclusive.  President  Foster  divided 
the  members  of  each  class  into  two  groups,  those  graduating 
with  distinction  and  those  graduating  without  distinction.  He 
found  that  for  every  class,  under  the  system  of  free  election 
then  in  vogue  at  Harvard,  the  latter  group  had  taken  a  greater 
proportion  of  their  work  in  snap  courses  than  the  former. 
In  the  case  of  most  of  the  classes  the  difference  in  question 
between  the  groups  was  definite  and  marked.*  The  cor- 
relation between  quality  of  grading  and  quality  of  students 
as  the  latter  was  ascertained  is  obviously  positive  in  the 
case  of  Dr.  Foster's  investigations.  However,  this 
may  be  due  entirely  to  the  fact  that  the  quality  of  the  stud- 
ents was  necessarily  determined  by  their  standings  in  elec- 
tive courses  rather  than  in  required  courses  as  at  Wil- 
liams College.  Doubtless  many  students  gained  distinc- 
tion by  selecting  snap  courses,  while  others  lost  that  honor 
by  selecting  heavy  courses.  Had  the  quality  of  the 
students  been  determined  on  the  basis  of  the  work  in  re- 
quired courses,  the  correlation  might  easily  have  been 
negative  in  this  case  also.  That  negative  correlation,  or 
even  absence  of  correlation,  between  the  quality  of  grad- 
ing and  the  quality  of  the  students  of  college  teachers  is 
sterling  evidence  of  the  need  of  scientific  grading  in  col- 
leges and  universities  goes  without  saying. 

The  need  for  a  scientific  distribution  of  the  grades 
of  college  students  having  been  presented,  our  next  ques- 
tion is  whether  such  a  thing  is  feasible,  mathematically 
and  practically.  If,  as  we  have  assumed,  the  abilities  or 
achievements  of  college  students  are  distributed  in  the 
form  of  the  probability  surface,  there  can  be  no  question 
regarding  the  mathematical  feasibility  of  the  undertaking. 
All  that  is  necessary  is  to  scale  off  equal  distances  for  the 
different  grades  to  be  given  on  the  zero  abscissa  between 
the  extremes  of  the  curve  and  to  compute  the  percentage 

*  Vide  Administration  of  the  College  Curriculum,  by  W.   T.    Foster,    pp 
217  ff.,  302-303. 

14 


of  the  surface  included  between  the  ordinates  at  the  end 
of  each  division.  These  percentages  will  be  identical  for 
all  curves  having  the  same  number  of  divisions  on  the 
abscissa  and  may  be  readily  calculated  by  use  of  tables. 
These  specifications  having  been  fixed  and  the  computa- 
tions made,  each  teacher  simply  arranges  his  students  in 
order  of  merit  and  assigns  the  different  grades  to  approx- 
imately the  proper  percentages  in  order.  A  plan  of  grad- 


Fiq.5 

ing  of  the  type  just  described  which  has  frequently  been 
recommended  for  adoption  by  men  interested  in  scientific 
grading  is  shown  in  figure  5.  The  five  divisions  on  the 
abscissa  are  all  approximately  equal,  save  that  the  middle 
one  corresponding  to  the  grade  C  is  somewhat  longer  in 
order  that  the  middle  group  of  students  may  comprise 
exactly  fifty  per  cent  of  the  entire  number.  In  accordance 
with  this  scheme  teachers  assign  the  grade  A  to  the  three 
per  cent  of  their  students  ranking  highest  in  the  same 

15 


class  or  subject,  the  grade  F  to  the  three  per  cent  rank- 
ing lowest  therein,  the  grades  B  and  D  to  the  twenty-two 
per  cent  ranking  next  highest  and  lowest  respectively, 
and  the  grade  C  to  those  in  the  middle  group  of  fifty  per 
cent.  Teachers  with  small  classes  do  not  necessarily  fol- 
low the  scheme  each  term  or  year,  but  rather  in  a  cumu- 
lative way  through  a  series  of  terms  of  years.  The  one 
criticism  the  writer  has  to  offer  here  upon  this  plan  is  that 
three  per  cent  seems  too  small  a  percentage  of  failures  to 
properly  motivate  a  considerable  class  of  students  well 
known  to  college  teachers.  The  scale,  however,  could 
readily  be  adjusted  to  meet  this  objection.  It  may  be 
suggested  further  that  where  there  is  no  desire  to  indicate 
different  degrees  of  failure  the  length  of  the  portion  of 
the  scale  representing  failure  may  without  violence  be 
fixed  somewhat  arbitrarily  without  reference  to  the  re- 
mainder. Doubtless  the  form  of  the  curve  in  figure  5 
should  be  slightly  modified  to  take  account  of  the  se- 
lective influence  of  the  college,  but  since  nothing  definite 
is  known  regarding  the  amount  of  this  influence  it  is  com- 
monly disregarded. 

We  may  be  assisted  in  attempting  to  answer  the  ques- 
tion of  the  practicality  of  a  scientific  or  normal  distribu- 
tion of  students'  grades  by  a  brief  description  of  a  system 
that  has  been  in  operation  at  the  University  of  Missouri 
since  1908.  The  system  in  question  was  introduced  by 
action  of  the  faculty,  and  its  administration  is  in  charge 
of  a  special  committee  of  the  faculty.  It  is  definitely  based 
upon  the  assumption  that  the  distribution  of  ability  or 
achievement  in  college  classes  is  approximately  normal. 
Every  teacher  is  expected  to  rank  the  students  in  his 
classes  in  order  of  merit  and  then  to  assign  the  grades 
E  and  S  (excellent  and  superior)  to  the  twenty-five  per 
cent  ranking  highest,  the  grades  I  and  F  (inferior  and 
failure)  to  the  twenty-five  per  cent  ranking  lowest,  and  the 
grade  M  (medium),  to  the  remaining  fifty  per  cent  be- 
tween. At  present  the  distribution  of  the  grades.  E  and  S 
and  I  and  F  among  the  groups  of  students  ranking  highest 
and  lowest  respectively  is  left  to  the  individual  teachers. 
The  committee  on  grading  after  the  close  of  each  semester 
publishes  a  statistical  table  showing  the  character  of  the 

16 


grading  of  each  teacher  for  the  semester  and  since  the  in- 
auguration of  the  present  system.  This  table  is  circulated 
among  the  faculty.  Teachers  whose  grading  deviates  mark- 
edly from  the  standards  established  are  called  to  account 
by  the  committee  and  asked  to  justify  their  failure  to  con- 
form. The  grading  of  teachers  of  small  classes  is  ex- 
pected to  conform  to  the  standards  only  when  taken  through 
a  series  of  semesters  or  years.  This  new  system  has  very 
largely  eliminated  the  diversity  of  practice  in  grading 
at  Missouri,  which  is  shown  in  table  I.  After  a  test  of 
more  than  two  years  the  system  was  declared  to  be  fairly 
successful  by  Professor  Meyer  and  to  be  becoming  more 
fully  so.*  A  similar  but  less  elaborate  system  was  intro- 
duced at  the  University  of  Iowa  in  1910.  Still  another 
similar  system  is  being  introduced  at  Reed  College  dur- 
ing the  present  academic  year.  Other  institutions  will 
not  be  slow  to  follow.  Given  a  faculty  on  the  whole  really 
desirous  of  improvement  and  with  conditions  carefully 
controlled,  as  at  the  University  of  Missouri,  and  there  is 
no  good  reason  why  the  distribution  of  students'  grades 
on  scientific  principles  should  not  be  practically  feasible. 
The  great  difficulty  is  to  overcome  the  inertia  of  past 
custom  and  individual  freedom.  The  actual  distribution 
of  the  grades  according  to  the  new  plan  is  easy.  The  gain 
in  accuracy,  standardization,  and  justice  are  worth  the  ef- 
fort involved  in  a  change  to  the  new  system  many  times 
over. 

Let  it  not  be  imagined,  however,  that  the  scientific 
distribution  of  grades  will  eliminate  all  the  difficulties  and 
discrepancies  encountered  in  the  administration  of  the 
grading  of  college  students.  The  introduction  of  such  a 
plan  of  grading  in  any  institution  must  be  considered  a 
big  stride  forward,  but  after  its  adoption  there  will  still 
remain  possibilities  of  improvement  in  the  field  under  con- 
sideration. Thus  the  wide  variations  among  small  college 
classes  in  quantitative  standards  of  requirements  and  ac- 
complishment will  not  be  very  greatly  affected  by  the 
new  plan.  It  is  not  too  much  to  say  that  some  college 
teachers  now  require  three  and  four  times  the  amount  of 


*Vide  Experiences  -with  the  grading  system  of  the  University  of  Missouri, 
by  Max  Meyer,  Science,  n.  s.  Vol.  33,  pp.  661  ff. 

17 


a  student's  time  and  energy  to  earn  a  given  amount  of 
credit  toward  graduation  that  some  other  teachers  in  the 
same  institution  demand  or  accept.  Snap  courses  and  the 
opposite  variety  do  abound,  and  the  latter  are  just  as  un- 
just and  just  as  conflicting  with  correct  standards  as  the 
former.  This  is  a  sad  state  of  affairs  for  academic  stand- 
ards, but  something  besides  correct  distribution  of  grades 
is  needed  to  adequately  remedy  it.  The  requirement  that 
a  teacher  giving  a  snap  course  or  the  opposite  distribute 
his  grades  in  the  form  of  the  probability  integral  will  of 
itself  by  no  means  raise  or  lower  the  standards  to  a  proper 
level,  though  without  doubt  it  will  ordinarily  contribute 
something  to  that  end.  Obviously  the  new  distribution 
of  grades  could  be  made  mechanically  with  no  change 
whatever  in  the  work  of  the  students.  Fear  of  failure  is 
not  the  only  factor  contributing  to  the  maintenance  of 
class  standards.  The  nature  and  amount  of  the  teacher's 
assignments  and  his  efficiency  in  the  classroom  as  a  teacher 
are  two  additional  factors  of  equal  and  greater  importance 
respectively.  However,  despite  the  relative  incapacity  of 
the  scientific  distribution  of  grades  to  standardize  amount 
of  work  in  college  classes,  such  distribution  does  render 
the  grading  in  the  variant  courses  under  consideration 
distinctly  more  accurate  and  just,  or  rather,  less  inaccurate 
and  unjust.  This  comes  from  the  fact  that  in  general 
teachers  of  snap  courses  are  required  to  lower  their  grades 
and  teachers  of  the  opposite  type  of  courses  are  corres- 
pondingly required  to  raise  their  grades,  which  is  all  well 
and  good  so  far  as  it  goes. 

An  extended  discussion  of  other  means  and  methods 
of  quantitatively  standardizing  requirements  and  achieve- 
ment in  college  courses  might  be  undertaken  here,  but 
such  a  discussion  would  carry  us  far  beyond  the  limits  of 
the  present  subject.  The  problem  of  such  standardiza- 
tion is  both  important  and  extremely  difficult.  The  sol- 
ution involves  first  of  all  full  recognition  by  teachers  of 
the  desirability  of  greater  uniformity  in  quantitative  stand- 
ards and  concerted  faculty  action  toward  that  end.  This 
goes  without  saying.  Another  effective  factor  in  the  so- 
lution of  this  and  other  college  problems  would  be  com- 
petent supervision  of  college  teaching.  It  is  realized  that 

18 


the  mere  suggestion  of  such  a  thing  will  be  considered 
heresy  by  many,  but  no  one  familiar  both  with  college 
teaching  and  with  the  effects  of  skillful  supervision  of 
teaching  in  elementary  and  secondary  schools  can  doubt 
the  potential  efficacy  of  supervision  in  the  college.  Super- 
vision of  instruction  is  distinct  from  administration.  The 
college  administrator  is  found  everywhere,  but  the  super- 
visor nowhere.  One  of  the  important  duties  of  a  super- 
visor of  college  teaching  would  certainly  be  the  standard- 
ization of  requirements  and  accomplishment  among  the 
different  classes. 

Another  very  important  advance  in  the  grading  of 
students  which  the  normal  distribution  of  grades  can  in 
no  way  bring  about  is  what  is  known  as  credit  for  quality. 
This  is  a  device  gradually  coming  into  favor  for  gradu- 
ating the  amount  of  credit  received  in  a  course  according 
to  the  quality  of  work  done  as  well  as  by  the  number  of 
hours  per  week  the  class  is  in  session.  There  is  a  very 
wide  difference  between  the  actual  achievement  of  a  stud- 
ent who  secures  the  required  number  of  credits  for  grad- 
uation with  an  average  grade  of  D+  or  C —  and  that  of 
the  student  who  gains  the  same  number  of  credits  with  an 
average  grade  of  A — ,  let  us  say.  It  is  probably  not  too 
much  to  say  on  the  basis  of  the  usual  values  of  these 
grades  that  the  actual  achievement  of  the  latter  in  the 
thing  the  college  stands  for  is  at  least  twice  that  of  the 
former;  yet  both  receive  the  same  degree  and  the  same  di- 
ploma. A  student  who  is  obliged  to  leave  at  the  end  of 
his  junior  year  with  an  average  grade  of  B+  or  A —  to 
his  credit  is  certainly  as  much  entitled  to  his  degree  on 
the  score  of  actual  attainment  as  the  one  who  finishes  in 
the  regular  way  with  an  average  grade  somewhere  below 
C.  From  these  considerations  both  the  justice  and  the 
standardizing  value  of  credit  for  quality  are  manifest.  In 
addition  it  has  a  distinct  educational  value  corrective  of 
unfortunate  habits  in  many  students  in  that  it  places  a  pre- 
mium on  thoroughness  and  penalizes  superficiality. 

The  plan  of  credit  for  quality  seems  to  have  been  first 
proposed  by  President  Hyde  of  Bowdoin  College  in  a 
magazine  article  ten  years  ago.*  It  was  seriously  advo- 
cated by  Professor  Cattell  of  Columbia  University  in 

*  Vide  Outlook,  Vol.  71,  pp.  886-889. 

19 


another  article  a  few  years  later.  t  In  1905  the  plan  was 
put  into  operation  at  the  University  of  North  Dakota,  but 
it  was  abandoned  in  most  respects  about  six  years  later. 
The  scheme  was  adopted  in  1905  at  Columbia  College, 
where  it  has  since  been  in  operation.  In  1908  credit  for 
quality  was  introduced  at  the  University  of  Missouri  in 
connection  with  the  plan  for  the  distribution  of  grades  in 
the  form  of  the  probability  curve.  It  is  now  being  intro- 
duced at  Reed  College.  The  schemes  at  these  different 
institutions  are  essentially  alike.  They  provide  that  stud- 
ents doing  superior  work  in  a  course  shall  receive  more 
than  the  normal  amount  of  credit  toward  graduation  and, 
what  is  equally  important,  that  those  doing  inferior  work 
shall  receive  less  than  the  normal  amount  of  credit.  Thus 
at  Missouri  where  the  five  grades  E,  S,  M,  I,  and  F  are 
now  given,  as  already  explained,  the  grade  E  carries  thirty 
per  cent  additional  credit,  the  grade  S  fifteen  per  cent 
additional  credit  ,  M  carries  the  normal  credit  ,  I  twenty 
per  cent  less  than  the  normal,  while  F  signifies  no  credit. 
The  other  schemes  differ  in  various  details  from  the  one 
here  described. 

There  can  be  no  doubt  that  under  certain  right  con- 
ditions credit  for  quality  is  an  extremely  valuable  feature 
in  the  grading  of  college  students.  In  fact,  it  is  an  essen- 
tial factor  in  thoroughly  scientific  grading.  Though 
the  correct  scale  of  credit  for  quality  has  not  been  de- 
termined, the  experience  of  the  future  may  be  trusted 
to  yield  an  approximation  to  it.  The  right  conditions  re- 
ferred to  are  the  scientific  distribution  of  grades  and  the 
quantitative  standardization  of  requirements,  so  far  as 
possible.  The  first  of  these  is  far  the  more  important. 
Without  scientific  distribution  of  grades  credit  for  quality 
is  apt  to  produce  very  disastrous  effects  by  greatly  multi- 
plying the  evils  of  snap  courses.  Not  only  are  high  grades 
awrarded  for  relatively  inferior  or  little  work,  but  these  un- 
earned grades  are  weighted  with  additional  credit.  Stud- 
ents are  given  two  strong  motives  instead  of  one  for  tak- 
ing such  courses,  and  teachers  seeking  popularity  and 
large  classes  are  doubly  tempted  to  bait  the  students.  If 
the  negative  correlation  between  the  quality  of  the  stud- 


/    tVide  Pop.  Sci.  Mo.,  Vol.  66,  pp.  375-37S. 

20 


ents  and  the  quality  of  grading  of  teachers  offering  elec- 
tive courses  which  was  found  to  prevail  at  Williams  Col- 
lege is  a  general  phenomenon  throughout  the  country,  the 
general  introduction  of  credit  for  quality  without  the  safe- 
guard of  scientific  distribution  of  grades  would  be  noth- 
ing short  of  an  educational  calamity.  Required  distribu- 
tion of  grades  in  the  form  of  the  probability  curve,  how- 
ever, by  confining  within  proper  limits  the  proportion  of 
each  grade  awarded,  would  not  only  render  credit  for 
quality  safe,  but  would  also  render  it  highly  effective  in 
accomplishing  the  results  desired  from  it.  The  scheme  of 
credit  for  quality  in  operation  for  a  number  of  years  at 
the  University  of  North  Dakota  was  abandoned  because 
of  precisely  the  evils  we  have  been  considering.*  It  is  distinctly 
in  point  to  add  that  at  this  institution  the  scheme  was  not 
safeguarded  by  a  correct  distribution  of  grades.  At  the 
University  of  Missouri  and  Reed  College  credit  for  quality 
is  properly  safeguarded  in  this  manner.  The  scientific 
distribution  of  grades,  however,  does  not  eliminate  snap 
courses,  as  has  been  indicated.  Low  standards  are  not 
necessarily  changed  by  it.  Snap  courses  retain  some  of 
their  power  to  work  ill  in  connection  with  a  scheme  of 
credit  for  quality  in  spite  of  normal  distribution  of  grades. 
A  few  moments  of  reflection  will  make  this  clear.  There- 
fore a  maximum  of  uniformity  in  class  standards,  correct 
of  course,  is  another  condition  which  should  be  realized 
as  a  basis  of  credit  for  quality,  as  well  as  for  other  good 
and  sufficient  reasons. 

Scientific  distribution  of  grades,  standardization  of 
requirements,  and  credit  for  quality  all  have  more  or  less 
important  bearings  upon  the  troublesome  problem  of 
properly  restricting  the  number  of  hours  of  work  which 
students  are  permitted  to  carry.  If  left  to  themselves  a 
large  proportion  of  students  would  register  for  course 
after  course  almost  without  limit.  This  tendency  under 
present  conditions  seems  to  require  some  artificial  check. 
It  is  recognized  that  without  some  such  limitation  under 
our  present  clumsy  systems  of  testing  and  grading  achieve- 
ments in  college  classes,  many  students  by  skilfully  choos- 
ing courses  and  complying  only  with  the  minimum  re- 


Cf .  Administration  of  the  College  Curriculum,  by  W.  T.  Foster,  p.  247. 

21 


quirements  in  courses  selected  could  easily  fulfil  the  formal 
requirements  for  graduation  in  a  scandalously  short  time. 
Hence  by  use  of  the  device  under  consideration  we  legis- 
late in  effect  that  students  must  remain  in  college  the 
usual  time  whether  they  employ  the  additional  time  to 
good  advantage  or  not.  Some  students  thus  required  to 
remain  in  college  longer  than  they  otherwise  would  do 
improve  the  extra  time  sufficiently  to  warrant  the  delay 
in  completing  the  requirements ;  others  do  not.  Another 
object  in  establishing  the  limitation  in  question  which  is 
much  more  sound  fundamentally  than  that  just  consid- 
ered is  to  shield  the  thoughtless  and  over-confident  stud- 
ents from  superficiality  and  failure.  On  the  whole  arbitrary 
limitations  of  the  number  of  hours  of  work  students  may 
carry  has  been  far  from  a  satisfactory  solution  of  the  prob- 
lem raised  above.  The  significance  of  the  problem  in 
this  connection  arises  from  the  fact  that  the  various  fea- 
tures of  scientific  grading  named  at  the  beginning  of  this 
paragraph  would  contribute  very  definitely  to  its  solution. 
Obviously  the  stiffening  of  snap  courses  and  the  award 
of  credit  according  to  quality  together  would  tend  to  reg- 
ulate automatically  the  number  of  hours  elected  by  stud- 
ents. Further,  they  would  be  a  fair  guarantee  that  all 
degrees  would  be  really  earned.  These  statements  should 
be  self-evident.  In  the  degree  to  which  scientific  grading 
could  be  perfected  the  need  of  artificial  limitations  of  the 
amount  of  work  carried  by  students  would  disappear. 

And  now  very  briefly  in  conclusion  let  us  connect  the 
special  problems  considered  in  these  pages  with  the  larger 
problem  of  which  they  are  only  a  part.  Somewhat  radical 
innovations  in  methods  and  system  of  grading  college  stud- 
ents have  been  suggested,  but  certainly  in  a  spirit  of  help- 
fulness rather  than  of  captious  criticism.  It  is  believed  that 
nothing  has  been  proposed  which  can  not,  should  not, 
and  will  not  in  due  time  be  carried  out.  The  movement  is 
now  definitely  under  way  in  progressive  institutions.  It 
is  but  one  aspect  of  the  growing  response  to  the  wide- 
spread demands  of  the  present  day  for  some  definiteness  in 
educational  standards  in  the  interest  altogether  of  in- 
creased efficiency  and  economy  in  the  education  of  our 
children  and  youth  and  in  the  service  of  society  through 

22 


education.  These  are  the  great  objective  points.  We  have 
frequently  heard  and  read  of  late  that  the  American  col- 
lege is  under  fire.  So  are  other  educational  institutions 
and  systems.  The  special  reference  in  these  pages  to  the 
grading  of  students  in  college  does  not  mean  that  the  col- 
lege alone  is  in  need  of  a  better  system  of  grading.  The 
same  remarks  are  also  applicable  to  this  phase  of  educa- 
tional administration  in  secondary  schools,  normal  schools, 
the  university  in  general,  and  elsewhere.  It  is  confidently 
believed  that  improvement  in  grading  is  one  of  the  im- 
portant lines  along  which  future  progress  in  educational 
standardization  will  occur. 


23 


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